(a) Field of the Invention
The present invention relates to receivers used in multifrequency signalling devices, especially between automatic telephone exchanges. It is more particularly concerned with time-division switching systems of the PCM type in which the speech channel is also used as the signalling channel. (b) Discussion of the Prior Art
In these multifrequency devices defined in accordance with C.C.I.T.T. recommendations, each signalling code element possesses two sinusoidal voice-frequency signals selected from q predetermined signals. There are therefore q[(q-1)/2] distinct codes which can represent, for example, q[(q-1)/2] decimal numbers.
Former techniques describe multifrequency signal receivers using filters and frequency-identification circuits of the analogue type. Such circuits are difficult to use because of the effects of component value dispersion, ambient conditions and ageing: they require considerable maintenance.
Since the present case is concerned with time-division switching, it is preferable to use digital techniques, since the bifrequency signals are processed in the same manner as the speech signals.
One feature of the present invention is therefore a multifrequency signal receiver using digital techniques for identifying without ambiguity the signalling frequencies from real signals in the time continuum. As in the case of all digital circuits of this type, such a receiver is relatively insensitive to the effects of interference and moreover its adjustment in the factory and its maintenance are very simple.
The advantages of digital techniques are so great that it has been proposed in certain known systems to sample and linearly encode in binary form multifrequency signals appearing in analogue form upon reception. In particular, a receiver of this type is described in the French Pat. No. 2295665 entitled "Recepteur numerique de signaux multifrequences" (Digital Receiver for Multifrequency Signals) filed on Dec. 18, 1974.
The means used for the present invention include a discrete Fourier transform (DFT) calculation device which converts a series of real-time samples whose amplitudes y(k) are quantified and encoded into a series of real frequency-characterized signals. Such a device therefore behaves in the present case as a group of q filters for recognizing the presence or absence of two frequencies amongst the q signalling frequencies.
It is always possible to perform this transformation with a general-purpose computer. However, and this is precisely the main purpose of the invention, the special structure of certain multifrequency codes can allow considerable simplification of the calculations and the production of special-purpose computers consisting of fewer components.
In order to fix one's ideas, this type of situation occurs for example with the SOCOTEL multifrequency (SOCOTEL MF) system which, in addition to a 1900 Hz control frequency f.sub.c, has six frequencies associated in pairs to produce 15 code combinations. These six frequencies lie between 700 and 1700 Hz in arithmetical progression.
Since the largest common divisor of the numbers of this progression is 100, it is possible to receive 7 to 17 complete sinusoidal periods in an interval T.sub.0 =1/.DELTA.F.sub.O =10 ms. It may be inferred that taking an average value over a sufficiently long period vT.sub.0, determination of the code frequencies results from the calculation of the spectral composition during a succession of v periods.
In general, according to Shannon's theroem, the sampling frequency F.sub.E of the processed analog signal in sampled digital systems should be at least twice the maximum frequency of the transmitted band (i.e. 4 kHz for telephone systems). In a PCM system, F.sub.E is therefore 8000 Hz.
It is immediately seen that in the case of the SOCOTEL MF system, .DELTA.F.sub.0 is a divisor of F.sub.E :F.sub.E /.DELTA.F.sub.0 =80. The common solution for determining the spectral composition of a received time-division signal by using the DFT consists of performing with a computer all the operations defined by the relationship (1) ##EQU1## where:
N=F.sub.E /.DELTA.F.sub.O
n=0, 1, 2 . . . (N-1)
k=0, 1, 2 . . . (N-1)
In this relationship, Y(n) represents the series of spectral samples, k is the order of a sample of the time-division signal having an amplitude y(k) during the interval T.sub.0, and N represents the number of samples to be used during the interval T.sub.0 for isolating without ambiguity only those spectrum components corresponding to T.sub.O.
According to the Nyquist criterion, similar to Shannon's theorem, this last condition is satisfied when F.sub.E is at least twice the maximum frequency of the time-division signal, i.e. 2f.sub.p.
In the case of the SOCOTEL MF system, f.sub.p =1700 Hz, whence F.sub.E &gt;2f.sub.p and N=F.sub.E /.DELTA.F.sub.O =F.sub.E T.sub.O =80.
A special property of the DFT associated with the periodic character (T.sub.O) of the time-division signal (.DELTA.F.sub.O) of the spectrum is seen in the following two relationships: EQU y(k)=y(k.+-.mN) (2) EQU Y(n)=Y(n.+-.mN) (3)
where m=0, 1, 2, . . .
In certain cases, these relationships make it possible to simplify the determination of the spectrum components by relationship (1).
In general, the time-division samples can be represented in symbolic form y.sub.r (k)+jy.sub.i (k), and the determination of each of the terms of the second term of relationship (1) requires in principle 4 multiplications and 2 additions in order to calculate Y(n)=Y.sub.r (n)+jY.sub.i (n).
It is seen that the calculation of all the values Y.sub.i (n) and Y.sub.r (n) requires Q=(4+2)N.sup.2 operations.
By means of an algorithm proposed by Cooley and known as the fast Fourier transform (FFT), it is possible to reduce Q considerably when N is written: N=a.sup..alpha. .times.b.sup..beta. .times.c.sup..gamma. .times.. . . , where a, b, c, . . . are the natural prime numbers and .alpha., .beta., .gamma., . . . are small-value exponents. In this case: EQU Q=(4+2)N (.alpha.a+.beta.b+.gamma.c . . . ).
The reduction is considerable when N=2.sup..alpha.. EQU Q=(4+2)(2Nlog.sub.2 N).
For example, if N=80, the simple application of formula (1) requires 4.times.6400 multiplications and 2.times.6400 additions.
If the FFT algorithm is applied: EQU N=2.sup.4 .times.5; (.alpha.a+.beta.b)=13.
4.times.1040 multiplications and 2.times.1040 additions are still required for calculating all the Y.sub.1 (n) and Y.sub.2 (n) terms.
If, however, N.sub.T can be reduced by an artifice to 16, the number of samples which define the digital spectral composition during the interval T.sub.0 =1/.DELTA.F.sub.0 =10 ms, the determination of the complex Y spectrum only requires: 4.times.128 multiplications and 2.times.128 additions at the most.
The properties of the FFT are described in "Theorie et Application de la transformation de Fourier rapide" (Theory and Application of the Rapid Fourier Transform) by J. Lifermann (Masson--Paris 1977) and also in Chapter 7 of "Introduction to Digital Filtering" (John Wiley and Sons--London--New York--1975).